Constitutive relations for dynamic material instability at finite deformation (Q2774045)

The author presents a mathematically coherent formulation for instability phenomena in materials with constitutive equations depending on the second displacement gradient. Some results of the dynamical systems theory are used to define and investigate material stability and instability problems. The paper is organized in the following way:NEWLINENEWLINE In Section 2 ``The basic equations for a large deformation'', the kinetic equations for large deformation, the Cauchy equations of motion, and the constitutive equations of the material are presented. The wave dynamic conditions and dynamical systems conditions are derived in Section 3 ``A wave dynamic theory of constitutive equations''. In Section 4 ``Material instability and dynamical systems'', a material instability investigation is made for finite uniaxial displacement for a particular constitutive equation.